I understand the problem of reusing the same key in the one-time pad if the cleartext message only contains characters such as A-Z, a-z and spaces.
But what if our cleartext is composed of arbitrary bytes? Which type of attack can we make to find the key or/and decrypt the ciphertext?
I think you misunderstand the concept of the one-time pad encryption method since the one-time pad treats messages like a binary sequence.
What is done is actually for a message $m$ (this message could be an image, a text, anything, ...), you use its binary representation and XOR its binary value with a binary key $k$ : $m$ $\oplus$ $k$. So it doesn't matter what kind of characters your message contains, you still can't break the security of the scheme when using the same key.
Check out this question: Taking advantage of one-time pad key reuse?
Welcome!
Reusing the same key is fatal to the one-time pad--it does not matter which characters were used in the creation of the truly-random key, from all the possible values on the keyboard, just numbers, just letters, binary, whatever. It can only be used once: that is why they call it the one-time pad.
By definition the one-time pad was generated in a truly random manner. Given such a key that has been properly safeguarded, there is no known attack against it if the one-time pad is properly applied--the key must be at least as long as the plaintext. It is often called the perfect cipher.
